求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
本次共计算 1 个题目：每一题对 y 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(e^{x} - 6e^{3x})cos(e^{x} + lg(y)) + (e^{4x} - 7e^{2x})sin(e^{x} + lg(y)) 关于 y 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{x}cos(e^{x} + lg(y)) - 6e^{3x}cos(e^{x} + lg(y)) + e^{4x}sin(e^{x} + lg(y)) - 7e^{2x}sin(e^{x} + lg(y))\right)}{dy}\\=&e^{x}*0cos(e^{x} + lg(y)) + e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) - 6e^{3x}*0cos(e^{x} + lg(y)) - 6e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) + e^{4x}*0sin(e^{x} + lg(y)) + e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) - 7e^{2x}*0sin(e^{x} + lg(y)) - 7e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})\\=& - \frac{e^{x}sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}sin(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}cos(e^{x} + lg(y))}{yln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - \frac{e^{x}sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}sin(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}cos(e^{x} + lg(y))}{yln{10}}\right)}{dy}\\=& - \frac{-e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}*0sin(e^{x} + lg(y))}{yln{10}} - \frac{e^{x}*-0sin(e^{x} + lg(y))}{yln^{2}{10}} - \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} + \frac{6*-e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}*0sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}*-0sin(e^{x} + lg(y))}{yln^{2}{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} + \frac{-e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{e^{4x}*0cos(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}*-0cos(e^{x} + lg(y))}{yln^{2}{10}} + \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} - \frac{7*-e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{7e^{2x}*0cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}*-0cos(e^{x} + lg(y))}{yln^{2}{10}} - \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}}\\=&\frac{e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}}\right)}{dy}\\=&\frac{-2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{e^{x}*0sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{e^{x}*-0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} - \frac{-2e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{x}*0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{x}*-2*0cos(e^{x} + lg(y))}{y^{2}ln^{3}{10}} - \frac{e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} - \frac{6*-2e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{6e^{3x}*0sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{6e^{3x}*-0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} + \frac{6*-2e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{6e^{3x}*0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{6e^{3x}*-2*0cos(e^{x} + lg(y))}{y^{2}ln^{3}{10}} + \frac{6e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} - \frac{-2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{e^{4x}*0cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}*-0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} - \frac{-2e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}*0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}*-2*0sin(e^{x} + lg(y))}{y^{2}ln^{3}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} + \frac{7*-2e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{7e^{2x}*0cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}*-0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} + \frac{7*-2e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}*0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}*-2*0sin(e^{x} + lg(y))}{y^{2}ln^{3}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}}\\=& - \frac{2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{e^{x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{12e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{18e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{14e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{21e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - \frac{2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{e^{x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{12e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{18e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{14e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{21e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}}\right)}{dy}\\=& - \frac{2*-3e^{x}sin(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{2e^{x}*0sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{2e^{x}*-0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{2e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} + \frac{3*-3e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{3e^{x}*0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{3e^{x}*-2*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{3e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} + \frac{-3e^{x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{x}*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{e^{x}*-3*0sin(e^{x} + lg(y))}{y^{3}ln^{4}{10}} + \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} + \frac{12*-3e^{3x}sin(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{12e^{3x}*0sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{12e^{3x}*-0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{12e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} - \frac{18*-3e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{18e^{3x}*0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{18e^{3x}*-2*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{18e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} - \frac{6*-3e^{3x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{6e^{3x}*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{6e^{3x}*-3*0sin(e^{x} + lg(y))}{y^{3}ln^{4}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} + \frac{2*-3e^{4x}cos(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{2e^{4x}*0cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{2e^{4x}*-0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{2e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} + \frac{3*-3e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{3e^{4x}*0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{3e^{4x}*-2*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{3e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} - \frac{-3e^{4x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{e^{4x}*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{e^{4x}*-3*0cos(e^{x} + lg(y))}{y^{3}ln^{4}{10}} - \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} - \frac{14*-3e^{2x}cos(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{14e^{2x}*0cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{14e^{2x}*-0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{14e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} - \frac{21*-3e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{21e^{2x}*0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{21e^{2x}*-2*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{21e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} + \frac{7*-3e^{2x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{7e^{2x}*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{7e^{2x}*-3*0cos(e^{x} + lg(y))}{y^{3}ln^{4}{10}} + \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}}\\=&\frac{6e^{x}sin(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{11e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{6e^{x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{4}{10}} - \frac{36e^{3x}sin(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{66e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{36e^{3x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{4}{10}} - \frac{6e^{4x}cos(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{11e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{6e^{4x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{4}{10}} + \frac{42e^{2x}cos(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{77e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{42e^{2x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(e^{x} - 6e^{3x})cos(e^{x} + lg(y)) + (e^{4x} - 7e^{2x})sin(e^{x} + lg(y)) 关于 y 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{x}cos(e^{x} + lg(y)) - 6e^{3x}cos(e^{x} + lg(y)) + e^{4x}sin(e^{x} + lg(y)) - 7e^{2x}sin(e^{x} + lg(y))\right)}{dy}\\=&e^{x}*0cos(e^{x} + lg(y)) + e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) - 6e^{3x}*0cos(e^{x} + lg(y)) - 6e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) + e^{4x}*0sin(e^{x} + lg(y)) + e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)}) - 7e^{2x}*0sin(e^{x} + lg(y)) - 7e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})\\=& - \frac{e^{x}sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}sin(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}cos(e^{x} + lg(y))}{yln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - \frac{e^{x}sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}sin(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}cos(e^{x} + lg(y))}{yln{10}}\right)}{dy}\\=& - \frac{-e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}*0sin(e^{x} + lg(y))}{yln{10}} - \frac{e^{x}*-0sin(e^{x} + lg(y))}{yln^{2}{10}} - \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} + \frac{6*-e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}*0sin(e^{x} + lg(y))}{yln{10}} + \frac{6e^{3x}*-0sin(e^{x} + lg(y))}{yln^{2}{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} + \frac{-e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{e^{4x}*0cos(e^{x} + lg(y))}{yln{10}} + \frac{e^{4x}*-0cos(e^{x} + lg(y))}{yln^{2}{10}} + \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}} - \frac{7*-e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{7e^{2x}*0cos(e^{x} + lg(y))}{yln{10}} - \frac{7e^{2x}*-0cos(e^{x} + lg(y))}{yln^{2}{10}} - \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{yln{10}}\\=&\frac{e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{e^{x}sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}}\right)}{dy}\\=&\frac{-2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{e^{x}*0sin(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{e^{x}*-0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} - \frac{-2e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{x}*0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{x}*-2*0cos(e^{x} + lg(y))}{y^{2}ln^{3}{10}} - \frac{e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} - \frac{6*-2e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{6e^{3x}*0sin(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{6e^{3x}*-0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} + \frac{6*-2e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{6e^{3x}*0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{6e^{3x}*-2*0cos(e^{x} + lg(y))}{y^{2}ln^{3}{10}} + \frac{6e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} - \frac{-2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{e^{4x}*0cos(e^{x} + lg(y))}{y^{2}ln{10}} - \frac{e^{4x}*-0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} - \frac{-2e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}*0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} - \frac{e^{4x}*-2*0sin(e^{x} + lg(y))}{y^{2}ln^{3}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}} + \frac{7*-2e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{7e^{2x}*0cos(e^{x} + lg(y))}{y^{2}ln{10}} + \frac{7e^{2x}*-0cos(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln{10}} + \frac{7*-2e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}*0sin(e^{x} + lg(y))}{y^{2}ln^{2}{10}} + \frac{7e^{2x}*-2*0sin(e^{x} + lg(y))}{y^{2}ln^{3}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{2}ln^{2}{10}}\\=& - \frac{2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{e^{x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{12e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{18e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{14e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{21e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - \frac{2e^{x}sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{e^{x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{12e^{3x}sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{18e^{3x}cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{6e^{3x}sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{2e^{4x}cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{3e^{4x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{e^{4x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{14e^{2x}cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{21e^{2x}sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{7e^{2x}cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}}\right)}{dy}\\=& - \frac{2*-3e^{x}sin(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{2e^{x}*0sin(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{2e^{x}*-0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{2e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} + \frac{3*-3e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{3e^{x}*0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{3e^{x}*-2*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{3e^{x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} + \frac{-3e^{x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{x}*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{e^{x}*-3*0sin(e^{x} + lg(y))}{y^{3}ln^{4}{10}} + \frac{e^{x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} + \frac{12*-3e^{3x}sin(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{12e^{3x}*0sin(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{12e^{3x}*-0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{12e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} - \frac{18*-3e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{18e^{3x}*0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{18e^{3x}*-2*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{18e^{3x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} - \frac{6*-3e^{3x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{6e^{3x}*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{6e^{3x}*-3*0sin(e^{x} + lg(y))}{y^{3}ln^{4}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} + \frac{2*-3e^{4x}cos(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{2e^{4x}*0cos(e^{x} + lg(y))}{y^{3}ln{10}} + \frac{2e^{4x}*-0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{2e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} + \frac{3*-3e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{3e^{4x}*0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} + \frac{3e^{4x}*-2*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{3e^{4x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} - \frac{-3e^{4x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{e^{4x}*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{e^{4x}*-3*0cos(e^{x} + lg(y))}{y^{3}ln^{4}{10}} - \frac{e^{4x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}} - \frac{14*-3e^{2x}cos(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{14e^{2x}*0cos(e^{x} + lg(y))}{y^{3}ln{10}} - \frac{14e^{2x}*-0cos(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{14e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln{10}} - \frac{21*-3e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{21e^{2x}*0sin(e^{x} + lg(y))}{y^{3}ln^{2}{10}} - \frac{21e^{2x}*-2*0sin(e^{x} + lg(y))}{y^{3}ln^{3}{10}} - \frac{21e^{2x}cos(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{2}{10}} + \frac{7*-3e^{2x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{7e^{2x}*0cos(e^{x} + lg(y))}{y^{3}ln^{3}{10}} + \frac{7e^{2x}*-3*0cos(e^{x} + lg(y))}{y^{3}ln^{4}{10}} + \frac{7e^{2x}*-sin(e^{x} + lg(y))(e^{x}*0 + \frac{1}{ln{10}(y)})}{y^{3}ln^{3}{10}}\\=&\frac{6e^{x}sin(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{11e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{6e^{x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{x}cos(e^{x} + lg(y))}{y^{4}ln^{4}{10}} - \frac{36e^{3x}sin(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{66e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{36e^{3x}sin(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{6e^{3x}cos(e^{x} + lg(y))}{y^{4}ln^{4}{10}} - \frac{6e^{4x}cos(e^{x} + lg(y))}{y^{4}ln{10}} - \frac{11e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} + \frac{6e^{4x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} + \frac{e^{4x}sin(e^{x} + lg(y))}{y^{4}ln^{4}{10}} + \frac{42e^{2x}cos(e^{x} + lg(y))}{y^{4}ln{10}} + \frac{77e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{2}{10}} - \frac{42e^{2x}cos(e^{x} + lg(y))}{y^{4}ln^{3}{10}} - \frac{7e^{2x}sin(e^{x} + lg(y))}{y^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
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